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Longman Dictionary of Contemporary English
non-denominational
adjective
EXAMPLES FROM CORPUS
▪ Archbishop McHale, who opposed the non-denominational system, was hoping for a verdict to support his views.
▪ It was basically envisaged to be of national proportions as well as non-denominational, with religious instruction given in separate classes.
▪ Religious education in these schools is officially non-denominational or biblically based and loyalist sentiments are promoted.
▪ St Paul's is a national non-denominational society with 75 ministers.
▪ These schools were to be non-denominational and open to inspection.
▪ We've opened a non-denominational advisory centre for teenagers.
Douglas Harper's Etymology Dictionary
non-denominational

also nondenominational, 1893, from non- + denominational.

Wiktionary
non-denominational

a. (alternative spelling of nondenominational English)

Wikipedia
Non-denominational

A non-denominational person or organization is not restricted to any particular or specific religious denomination.

Usage examples of "non-denominational".

The Rebels buried the dead, and chaplain read a short non-denominational service.